Returns an array of probabilities each representing F(x_i). The CDF is evaluated for each point in the input array x and the probabilities are returned in the returned array.

open fun cdf(interval: Interval): Double

Returns the probability of being in the interval, F(upper limit) - F(lower limit) Be careful, this is Pr{lower limit < = X < = upper limit} which includes the lower limit and has implications if the distribution is discrete

open fun cdf(x1: Double, x2: Double): Double

Returns the Pr{x1 <= X <= x2} for the distribution. Be careful, this is Pr{x1 <= X <= x2} which includes the lower limit and has implications if the distribution is discrete

open override fun cdf(x: Double): Double

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

complementaryCDF

open fun complementaryCDF(x: Double): Double

Computes the complementary cumulative probability distribution function for given value of x. This is P{X > x}

domain

open override fun domain(): Interval

instance

open override fun instance(): GeneralizedBeta

invCDF

open override fun invCDF(p: Double): Double

Provides the inverse cumulative distribution function for the distribution

open fun invCDF(probabilities: DoubleArray): DoubleArray

Computes x_p where P(X <= x_p) = p for the supplied array of probabilities. Requires that the values within the supplied array are in (0,1)

likelihood

open fun likelihood(data: DoubleArray): Double

Assuming that the observations in the array data are from a random sample, this function computes the likelihood function. This is computed using as the sum of the log-likelihood function raised to e. Implementation may want to specify other computationally efficient formulas for this function or (most likely) the sum of the log-likelihood function.

logLikelihood

open override fun logLikelihood(x: Double): Double

Computes the natural log of the pdf function evaluated at x. Implementations may want to specify computationally efficient formulas for this function.

mean

open override fun mean(): Double

Returns the mean or expected value of a distribution

parameters

open override fun parameters(): DoubleArray

Returns the parameters as an array params0 the alpha shape parameter params1the beta shape parameter params2 the minimum of the range params3 the maximum of the range

open override fun parameters(params: DoubleArray)

Changes the parameters to the supplied values params0 the alpha shape parameter params1the beta shape parameter params2 the minimum of the range params3 the maximum of the range

fun parameters(alphaShape: Double, betaShape: Double, theMinimum: Double = min, theMaximum: Double = max)

Changes the parameters to the supplied values

pdf

open override fun pdf(x: Double): Double

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

randomVariable

open override fun randomVariable(stream: RNStreamIfc): RVariableIfc

open fun randomVariable(streamNum: Int): RVariableIfc

standardDeviation

open fun standardDeviation(): Double

Returns the standard deviation for the distribution as the square root of the variance if it exists

sumLogLikelihood

open fun sumLogLikelihood(data: DoubleArray): Double

Computes the sum of the log-likelihood function evaluated at each observation in the data. Implementations may want to specify computationally efficient formulas for this function.

toString

open override fun toString(): String

variance

open override fun variance(): Double

Returns the variance of the distribution if defined